I was asked to run a session for PGCE students using a kit of parts we make called Maths-for-a-Day. Basically, we took the content of the kits I had produced for the shopping centre events I organised during Maths Year 2000 and packaged them up in a box suitable for a school maths event. I asked for 6 volunteers from the group to staff the activities and the remainder were punters. All of the ‘staff’ were ‘selling’ their wares with gusto … 7 chairs in a line made a human version of the frogs puzzle, a mini-theatre was set up to run a ‘Countdown’ style competition. These two are designed to keep a group in one place and engage together. Two more stations had a range of geometric puzzles: Tower of Hanoi, Katamino, Tantrix, shape-by-shape and block-by-block and a double sided shut the box game next to a temptation to fold a sheet of paper in half 10 times to win a tub of chocolate. Calmer people came and stayed (one for most of the session) absorbed. On other other side, target maths and 24-game sets were set out and a pairs competed to solve puzzles.
Finally, one ‘staff’ member wandered round with a piar of big hands demonstrating the old finger maths method. The first group of ‘frogs’ gave up but one persisted and gathered another group together, some time passed before a loud cheer went up as they solved the problem. The whole gathering was sparky and full of life. A collections of wooden shape puzzles (T-puzzle, pyramid puzzle etc.) were left unattended in the middle of the room and a small group gathered. The T-puzzle is peculiarly engrossing. Four pieces only to make a T. Half an hour later, they still hadn’t cracked it.
I think the materials are nice, but really, it’s the dynamics which make this work. The group had to be prized away from what they were doing to sit down and talk about it after well over an hour of sustained activity. When we did this in shopping centres, shoppers stayed for hours doing maths puzzles even when they had just come for their groceries. We’vew done this in schools too, with real inner city comprehensive school kids and it’s just the same. Everyone can find an activity to suit them. No compulsion, no worries if they don’t like something and move on (but enough staff to make sure everything is given a fair chance and a bit of encouragement). Then everyone gets grabbed by something and the level of sutsained activity is qualitatively different to what can be achieved in a lesson where everyone is doing the same thing at the same time.
Critically, all of the problems need to be left open. A solved puzzle is a dead puzzle. Staff must always resists request for the answers. Their job is just to encourage activity. Students cannot solve simple problems in exams, often simply because they give up. Getting grabbed by a good puzzle feeds the desire to NOT give up and maths is full of knotty problems where just keeping going is essential. Puzzles like this are an excellent training in this vital maths and maths-at-school (i.e. maths exams!) skill.
Clearly, you cannot throw this level of resourcing at every lesson. But if you kicked off the term with an event like this, you have set up enough maths for the term: indices and standard form from the paper folding activity. Any level of sophisticated arithmetic leading into algebra with the target maths and countdown. Two cracking investigations leading to proof with the Towers of Hanoi and the Frogs (which players will by now have ‘felt’ the geometry of, which is an essential pre-requisite to setting up a proof). Area investigations with the Tangram based shape-by-shape and a full investigation into -ominoes using the hexomino based Katamino game (which includes the possibility for extensive transformational geometry work).
It was really exciting to see how the next tranche of new teachers were really excited by the possibility to engage their future students, although frustrated by the worry that target driven schools will be worried to work this way. But led by the activities which are so grabby that kids are hooked and with sophisticated mathematical trajectories, some day all maths could be taught this way! After the Maths Year 2000 experience we wrote up all of the thinking about structuring and organising events like this together with all of the extra print and logistics materials and made the handbook for Maths for a Day, so open the box, read and get going!